RE: mountain lions in NY??
I have seen a couple of bobcat through the years in WNY, 1 with a couple of kittens crossing a logging rd in Humphrey, NY in Golden Hill State Forest - Great state land for Turkey, and one in Deleven at a tree famr Blue Hill Arboretum (don't know if I spelled that right or not) this one I saw just last fall while scouting before bow season.
Bill Yox, I used to trap coyotes and Fox real hard every year but, I have three kids, a career, and a fiance now - trapping kind of took a back burner. I still hunt them mwith my brother pretty hard though. Calling them is the primary way people hun them around me but I know of a couple people who put on drives like you would for deer, and one guy over near Springville, NY uses dogs but that's the only person I have ever heard of local that uses dogs on yotes. I haven't heard of any real competitions though besides the casual - i shot more than you did try and top that - type between hunting partners.
I see the Gray fox population go down but, the reds don't seem to be impacted by the coyotes as much as the grays. My opinion is that grays think they are as tough as coyotes - The Mighty Mouse Syndrom - they are real aggressive and I think they might just compete with the coyotes a little more for food than the reds do and the coyotes end up winning that battle - I think the reds are a little more shy and tend to just stay away from the yotes. Could be a combination of your reasoning and this - can't really say.